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© 2012

Markov Bases in Algebraic Statistics

Benefits

  • Crucial guide for statisticians no matter previous exposure to algebra and algebraic statistics

  • Clear organization guides the reader through the 16 chapters with figures and tables

  • Shows topic in its broader context, beginning with introductory material

Book

Part of the Springer Series in Statistics book series (SSS, volume 199)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction and Some Relevant Preliminary Material

    1. Front Matter
      Pages 1-1
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 3-21
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 23-31
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 33-43
  3. Properties of Markov Bases

    1. Front Matter
      Pages 45-45
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 47-63
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 65-78
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 79-89
    5. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 91-105
  4. Markov Bases for Specific Models

    1. Front Matter
      Pages 107-107
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 109-128
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 129-157
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 159-179
    5. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 181-208
    6. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 209-227
    7. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 229-247
  5. Some Other Topics of Algebraic Statistics

    1. Front Matter
      Pages 249-249
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 251-259
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 261-273

About this book

Introduction

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels.

This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.

Satoshi Aoki obtained his doctoral degree from University of Tokyo in 2004 and is currently an associate professor in Graduate school of Science and Engineering, Kagoshima University.

Hisayuki Hara obtained his doctoral degree from University of Tokyo in 1999 and is currently an associate professor in Faculty of Economics, Niigata University.

Akimichi Takemura obtained his doctoral degree from Stanford University in 1982 and is currently a professor in Graduate School of Information Science and Technology, University of Tokyo.

Keywords

Algebra Algebraic Statistics Markov Bases Monte Carlo Toric Ideals

Authors and affiliations

  1. 1.Dept. Mathematics & Computer ScienceKagoshima UniversityKagoshimaJapan
  2. 2.Faculty of EconomicsNiigata UniversityNiigataJapan
  3. 3.University of TokyoTokyoJapan

About the authors

Satoshi Aoki obtained his doctoral degree from the University of Tokyo in 2004 and is currently an associate professor in the Graduate School of Science and Engineering, Kagoshima University.

Hisayuki Hara obtained his doctoral degree from the University of Tokyo in 1999 and is currently an associate professor in the Faculty of Economics, Niigata University.

Akimichi Takemura obtained his doctoral degree from Stanford University in 1982 and is currently a professor in the Graduate School of Information Science and Technology, University of Tokyo.

Bibliographic information

Industry Sectors
Finance, Business & Banking
Pharma

Reviews

From the reviews:

“The book by Aoki, Hara, and Takemura presents a thorough introduction to Markov chain Monte Carlo tests for discrete exponential families, focusing on the concept of Markov bases. It is an authoritative and highly readable account of this field. … This text is the definitive reference on the subject, aimed principally at statisticians interested in Markov chain algorithms for sampling from discrete exponential families and its various applications … . It could also be used as a textbook for an advanced seminar on the subject.” (Luis David García-Puente, Mathematical Reviews, December, 2013)